New stability results for long-wavelength convection patterns

Details New stability results for long-wavelength convection patterns New stability results for long-wavelength convection patterns

1997-12-16

arxiv.org/abs/patt-sol/9712006v1

Nonlinear Sciences

Pattern Formation and Solitons

25 pages, 8 figures

Scientific paper

We consider the transition from a spatially uniform state to a steady, spatially-periodic pattern in a partial differential equation describing long-wavelength convection. This both extends existing work on the study of rolls, squares and hexagons and demonstrates how recent generic results for the stability of spatially-periodic patterns may be applied in practice. We find that squares, even if stable to roll perturbations, are often unstable when a wider class of perturbations is considered. We also find scenarios where transitions from hexagons to rectangles can occur. In some cases we find that, near onset, more exotic spatially-periodic planforms are preferred over the usual rolls, squares and hexagons.

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